Training devices for trajectory-based sports

ABSTRACT

Methods and apparatus related to improving player performance for trajectory-based sports are described. In particular, sporting devices are described that can be utilized to improve player performance in basketball. The sporting devices can include a camera-based system configured to capture and analyze the trajectory of a shot taken by a player. The camera-based system can be configured to provide feedback that allows a player to optimize the trajectory mechanics associated with shooting a basketball. In one embodiment, the camera-based system can be used in conjunction with a training aid that is attached to a basketball rim. The training aid can be configured to improve the trajectory mechanics of individuals utilizing the modified basketball rim to practice their shooting.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §119(e) from co-pendingU.S. Provisional Patent Application No. 61/286,474, filed Dec. 15, 2010,titled “TRAINING DEVICES FOR TRAJECTORY-BASED SPORTS,” which isincorporated by reference and for all purpose.

This application is related to U.S. patent application Ser. No.12/127,744, filed May 27, 2008, by Marty, et al, title, “StereoscopicImage Capture with Performance Outcome Prediction in SportingEnvironments,” which is incorporated in its entirety and for allpurposes.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to devices and systems forsports training and entertainment and more specifically to a trajectorydetection and feed back systems and outcome prediction in sportingenvironments.

2. Description of the Related Art

In sports, player performance is primarily results based. A player issaid to be a good player when they produce a consistent result over somerange of circumstances. For instance, a professional basketball playermight be considered good when on average they produce a certain numberof points per game, rebounds, assists, etc., over the course of aseason. A player is said to be a great player when they produce aconsistent result in more extreme circumstances, such as, in achampionship or play-off game as well as providing good performances onaverage at other times. For example, some basketball players are knownfor being able to “take over a game” or impose their will on anotherteam in certain situations and are considered to be great for thisability.

The difference between a great and a good player is often described assome intangible quality, such as their will or drive to succeed.Sometimes even when a player produces what appears to be a resultconsistent with a great player, it is argued that the player is notreally great and their performance is a result of circumstances, such ashaving a really great supporting team. Further, in general, it is oftendifficult, in a quantifiable manner, to classify and distinguish theperformances between players of varying abilities or to distinguishbetween varying performances by the same player, in regards to answeringthe questions, such as, why is player 1 good while player 2 is average,why does the performance of a player vary so much, what is aquantifiable different between two performances?

The intangible nature of describing in a quantifiable manner thedifferences between performances in a sporting environment can befrustrating to players, coaches, broadcasters and spectators alike.Players want to be able identify in a quantifiable manner why their ownperformances vary from one to another or how their performance variesfrom a better player so that they can improve their performance. Coachesin team and individual sports want this information so that they canhelp their players improve. In team sports, coaches may want thisinformation as a way to exploit weaknesses possessed by opposingplayers. Broadcasters and spectators may want this information becauseit can add to the entertainment value of watching a sport. Further,spectators are also participants in many of the sports they watch, andthus the spectators may want to be able to quantify and compare theirown performances as well as compare their performance to theperformances of professional players or other participants of the sportin general.

In view of the preceding paragraphs, methods and apparatus are describedin the following paragraphs for determining quantifiable differencesbetween performances in a sporting environment that are not strictlyresults based. The methods and apparatus may include but are not limitedto methods and apparatus related to 1) capturing a performance in asporting environment, 2) analyzing a performance, 3) comparingperformances, 4) presenting results obtained from any analyses orcomparisons, 5) archiving captured performances, analyses andcomparisons and 6) providing simulations of performances using capturedand analyzed performance data.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be readily understood by the following detaileddescription in conjunction with the accompanying drawings, wherein likereference numerals designate like structural elements, and in which:

FIGS. 1A-1C are examples of graphic output formats related to theevaluation of a basketball trajectory performance including outcomeprediction.

FIG. 2 shows a top view of a basketball rim, backboard and net includingthe geometric center of the hoop and the geometric center of themake/miss zone.

FIG. 3A is plot of predicted shooting percentage for shots aimed atvarious locations within a basket ball rim.

FIGS. 3B-3E show trajectories drawn through the center of a basketballfor shots with entry angles that vary between 43 and 57 degreesrespectively.

FIG. 3F shows make/miss zones and shot locations within the make/misszone for the various shots shown in FIGS. 3B-3E.

FIGS. 3G and 3H show entry angle and shot location data measured for1000 players.

FIG. 4 shows top views of a backboard, basketball rim structure coupledto the backboard and net where a training aid is attached to the rim anda cross section of the training aid.

FIG. 5 is a diagram of a trajectory capture and feedback scenarioemploying a trajectory detection and feedback system.

FIG. 6 is a diagram of trajectory capture scenario employing variousembodiments of a trajectory detection and feedback system.

FIG. 7A is an illustration of coordinate system for determining amake/miss zone for basketball.

FIG. 7B is a side view of basketball shot passing through hoop atlocation of longest possible swish.

FIG. 7C is a side view of basketball shot passing through hoop atlocation of shortest possible swish.

FIG. 8 is an illustration of the swish zone for a 45-degree hoop entryangle.

FIG. 9 is an illustration of the geometry of rim-in shot off the backrim.

FIG. 10A is a plot of a make zone for a hoop entry angle of 45 degrees.

FIG. 10B is a plot of the make zone for a hoop entry angle of 25degrees.

FIG. 11 is a rear view of an experimental set-up for generatingbasketball trajectories.

FIG. 12 is a graph of shooting percentage as a function hoop entry anglegenerated both experimentally and analytically.

FIG. 13 shows standard deviations for launch angle and launch velocityas a function of entry angle for a number of experimentally generatedshots and a percentage of shots made for various entry angles.

FIG. 14 is a block diagram of an embodiment of a trajectory detectionand analysis system.

FIGS. 15A-15C are perspective drawings of one embodiment of a trajectorydetection and analysis system.

FIG. 16 is an information flow diagram of an embodiment for of atrajectory detection and analysis system.

DETAILED DESCRIPTION OF SELECTED EMBODIMENTS

Reference will now be made in detail to representative embodimentsillustrated in the accompanying drawings. It should be understood thatthe following descriptions are not intended to limit the embodiments toone preferred embodiment. To the contrary, it is intended to coveralternatives, modifications, and equivalents as can be included withinthe spirit and scope of the described embodiments as defined by theappended claims.

The following figures, 1A, 1B and 1C show the effect of the entry angleof the shot on the size of the make/miss zone. In FIG. 1A, the successcriterion that leads to make miss/zones, 302 a-302 e, include shots thathit the rim and went in as well as shots that didn't hit the rim andwent in. In FIG. 1B, the success criterion that leads to make/misszones, 303 a-303 e, include only shots that don't hit the rim. For 302a-302 e and 303 a-303 e, any shot where the center of the basketballpasses through the make zone as it enter the basketball hoop ispredicted to be a made shot, which is graphically represented in FIGS.1A, 1B and 1C. As is shown in the following section, “CalculatingBasketball Trajectory Dynamics: Basketball Swish/Make Analysis,” theprediction methodology is validated experimentally but may not be 100%accurate.

FIGS. 1A, 1B and 1C provide examples graphic output formats related tothe evaluation of a basketball trajectory performance for embodimentsdescribed herein. The make or miss zones for any entry angle may begenerated, but in FIGS. 1A and 1B increments of five degrees starting at30 degrees are shown. The location of shots in the make/miss zones forentry angles of 50, 45, 40, 35 and 30 are shown in FIGS. 1A and 1B. InFIG. 1C, make/miss zones for entry angles of 50, 45, 40 and 35 degreesare shown. In FIG. 1A, the outline of the area defining the make/misszone is shown. This make/miss zone includes shot that went in the hoopafter hitting the rim and shots that went in the hoop without touchingthe rim. The outline of each of the make/miss zone is drawn in the planedefining a top of a basketball hoop.

In FIG. 1B, the outline of the area of the make/miss zone, whichincludes only shots that went through the hoop with out touching the rimare shown. The make/miss zone is plotted for shots with entry angles of50, 45, 40 and 35 degrees. Again, the outlines of the make/miss zonesare drawn in the plane defining a top of a basketball hoop. In FIG. 1B,a graphical format showing the rim size from the point of view of thebasketball is shown. As the entry angle of the basketball as itapproaches the hoop decreases, the hoop appears smaller to thebasketball. The entry angle decreasing relates to a basketball shot witha decreasing arc. Drawing the hoop from the perspective of thebasketball is a way to graphically indicate that as the arc of the shotdecreases, there is less room for error in shooting the ball in regardsto placement of the ball between the front and the back of the rim.

At larger entry angles, the hoop appears larger to the basketball.Nevertheless, it has been observed the probability of making a shotdecreases when the arc of the shot becomes too large. The probability ofmaking a shot decreases for higher arced shots because changes in entryangle to the hoop at larger entry angles, which are associated withhigher arced shots, affects the position of the ball as it enters thehoop more than changes in entry angle at lower entry angles associatedwith lower arced shots. This effect is illustrated and described in moredetail with respect to FIGS. 3B-3F.

In FIG. 1C, the make zone is shown plotted within the center of thebasketball hoop. The make zone is generated analytically and is plottedfor different entry angles into the hoop. Any trajectory where thecenter of the basketball passes outside of the make zone, i.e., the areaoutside the make zone but within the basketball hoop will be a missedshot. Of course, shots outside of the basketball hoop will be a missedshot as well.

In FIG. 1C, the make zone is divided into two parts, a swish zone and aBRAD zone. The BRAD zone refers to shots where the basketball hits theBack of the Rim And goes Down through the basketball hoop. The Swishzone refers to shots that pass through the basketball hoop withouthitting the rim. It can be seen in FIG. 1C, as the trajectory of thebasketball flattens, i.e., the entry angle decreases, the rim becomesmore important for making the shot. The rim becomes more importantbecause as the entry angle decreases the percentage of made shotsinvolving the rim increases. At higher entry angles, such as 50 degrees,swish shots are a much higher percentage of the made shots as comparedto the made shots at the lower entry angles.

In FIGS. 3B-3F, a number of shot trajectories are simulated where all ofthe initial conditions are held constant accept for the arc of the shot.Each of the shots is a free throw released at a height of 7 feet. FIG.3B shows shots with trajectories that enter the basket from 43-47degrees, respectively. FIG. 3C shows shots with trajectories that enterthe basket from 48-52 degrees, respectively. FIG. 3D shows shots withtrajectories that enter the basket from 53-57 degrees, respectively.FIG. 3E shows the portion of the trajectories near the basket for eachof the shots between 43 and 57 degrees shown in FIGS. 3B-3D.

In the figures, the initial shot conditions are selected that lead toshots with entry angles from 43-57 degrees. Fifteen shots are shownwhere the entry angle of the shots increases by one degree incrementsfrom 43 to 57 degrees. Trajectories are drawn through the center of thebasketball. The trajectories start at the point where the shot is launchand end where the trajectory intersects the plane defined by thebasketball rim. As the entry angle of the shots increase the arc of eachshot also increases.

A comparison can be made between trajectories with entry angles thatdiffer by one degree. For instance, a comparison can be made between thetrajectories with entry angles of 44 and 45 degrees, 45 and 46 degrees,54 and 55 degrees and 55 and 56 degrees, respectively. It can be seen inthe figures that the distance between the locations at which thetrajectories intersect the basketball rim is much greater between the54, 55 and 56 degree shots as compared to the 44, 45 and 46 degreeshots. Thus, if a first player tries to shoot shots with an average arcof 55 degrees and a second player tries to shoot shots with an averagearc of 45 degrees, an error in the entry angle by the first player has amuch greater effect on location at which the trajectory of the shotintersects the plane of the basketball rim than the second player. Entryangle errors for the first player trying to shoot at a 55 degree entryangle is much more likely to lead to a missed shot than entry angleerrors for the player trying to shoot an arc of 45 degrees. This effectis further illustrated with respect to FIG. 3F.

FIG. 3F shows the locations at which the 43-47 degree trajectoriesintersect the plane of the basket ball rim where the locations areplotted on the make/miss zone for 45 degrees, the locations at which the48-52 degree trajectories intersect the plane of the basketball rim,where the trajectories are plotted on the make/miss zone for 50 degreesand the locations at which the trajectories of the 53-57 degreetrajectories intersect the plan of the basketball rim, where thelocations are plotted on the on the make/miss zone for 55 degrees. Itcan be seen in FIG. 3F that the make/miss zone at 55 degrees is greaterin area than the make/miss zone at 50 or 45 degrees. However, it canalso be seen in the figure that for shots with entry angles near 55degrees the effect of entry angle on shot location within the hoop ismuch greater than for shots with entry angles near 45 degrees. For theshots near 55 degrees, the changes in entry angle lead to shots fallingoutside the make/miss zone while at 45 degrees the changes in entryangle do not lead to shots falling outside of the make/miss zone. Thus,trying to shoot a shot with a higher entry angle, such as 55 degrees, isgoing to be more difficult on average to make than trying to shoot ashot with a lower entry angle, such as a 45 degree entry angle. Thisresult is consistent with experimental data and theoretical predictionsshown in FIGS. 12 and 13, which shows shooting percentage decreasing athigher shot entry angles.

The shape of the make/miss zone can vary depending on the release pointof the shot. FIG. 2 shows a top view of a basketball rim, backboard andnet including the geometric center of the hoop and the geometric centerof the make/miss zone. Because of back board/rim rebound effects, forshots released from an angle, such as either side of a straight-on shotas shown in the FIG. 2, the make/miss zone may not be symmetric around aline drawn from the shot location through the geometric center of thehoop, as it is for the straight on shots shown in FIG. 1A. Nevertheless,the geometric center of the make/miss zone may tend to move to the rightof its location, which is shown for a straight on shot, for shotsreleased from a location to the left of a straight on shot and thegeometric center of the make/miss zone may tend to move to the left forshots released from a location to the right of a straight on shot.

Returning to FIG. 1A, the geometric center of the hoop within the areaof the make/miss zone is shown. The make/miss zone includes shots thathit the rim in and go in as well as shots that pass through withouttouching the rim. The shot release point is for a shot released directlyin front of the basketball hoop. In FIG. 1A, it can be seen that thegeometric center of the hoop is not the geometric center of themake/miss zone. The geometric center of the make/miss zone is behind ordeeper in the basket than the geometric center of the hoop. At anoptimal shooting angle of about 43 degrees for a straight-on shot, thegeometric center of the make/miss zone is about 2 inches behind thegeometric center of the hoop.

The difference between the location of the geometric center of the hoopand geometric center of the make/miss zone suggests that it may bebeneficial to shoot the ball deeper in the basket behind the geometriccenter of the basket. It can be seen in FIG. 1A that the margin of errora shot aimed toward the center of the hoop is greater if the shot islong as opposed to if the shot is short. A more equal margin of errorfor short and long shots can be obtained when the shot is aimed deeper,i.e., behind the geometric center of the hoop.

As an example, at 30 degrees entry angle, the geometric center of thehoop is approximately at the boundary of the make/miss zone. Thus, ashot aimed toward the center of the hoop will miss if a shooting errorresults in the shot being short at all or slightly off-center. If theshooting error results in the shot being long, then margin of errorexists for the shot to still go in. The margin of error is much greaterfor the long shot than for the short shot. If the shot is aimed behindgeometric center of the hoop, such as toward the geometric center of themake/miss zone, the shooting error margins for long and short shots aremore equally balanced.

It is often observed that as a player gets tired over the course of agame, their shots are often short. If one player is trained to shootdeeper in the basket behind the geometric center of the hoop and anotherplayer is trained to shoot at the geometric center of the hoop, then asboth players tire and their shots are more likely to go shorter, theplayer trained to shoot deeper in the basket may have an advantage overthe player trained to shoot at the geometric hoop center. The playerthat is trained to shoot deeper in the basket may have an advantage overthe other player because the player trained to shoot deeper would have agreater margin of error on their short shots than the player trained toshoot at the geometric center of hoop.

The strategy above assumes that for a given player the odds of making ashooting error, such as ‘long or short’ and ‘left or right,’ are equallylikely for a given player. With an equal distribution among theprobability of making a shooting error, it may be beneficial to balancethe error margins for each type of shooting error that can occur. Forinstance, the player has a similar margin of error for a shooting errorthat results in the shot being short of its intended target or for ashooting error that results in the shot being past its intended target,i.e., long. If it were demonstrated for a particular player that theirshooting errors were biased in a particular manner, such as the playerwas much more likely overshoot the target they were aiming for ratherthan undershoot their shot, it might be more advantageous to utilizeanother shooting strategy for this type of player.

As an example of a shooting strategy for a player with an unequalshooting error distribution, for a player that always tends to shoottheir shots long, it may be beneficial to implement a shooting strategythat favors increasing the error margins for long shots as opposed toshort shots, such as training to aim their shots more towards the centerof the hoop. Conversely, if a player tended to make more shooting errorsshort, than for this type of player it may be advantageous to devise ashooting strategy where they are trained to aim deeper in the basket ascompared to a player equally likely to miss a shot short or a long shot.Similarly, a player that tends to have more shooting errors to the leftas opposed to shooting errors to the right might gain an advantage ifthey trained to aim for a point in the basket that is slightly right ofthe center of the hoop rather than straight on.

Besides player variations, a likely hood of a shooting error may beaffected by shooting physics. As described above, it takes more force toshoot a shot longer than a shot shorter. As the force used to generate ashot increases, velocity errors can become more important. Thus, for agiven target location within the hoop, the error distribution for longshots, i.e., past the target location, as a function of the distancefrom the target location may differ with distance differently than shortshots as a function of distance from the target location. For instance,the error rate as a function of distance for long shots may increasefaster than the error rate as a function of distance for short shotsbecause of the increasing forces associated with long shots. Based uponthe error distribution, a target location can be selected that optimizestheir chance of making a shot. As described above, this target locationmay be different than the geometric center of the hoop and may be closerto the geometric center of the make/miss zone but may not be exactlyequal to the geometric center of the make/miss zone.

In general, shooting strategies can be developed for players in generalor tailored to an individual player. A general shooting strategy can bedeveloped based on an error analysis of the types of errors players as agroup tend to make and then a shooting location within the hoop, whichaccounts for the make/miss zone, can be tailored that optimizes theirchances of making shots based upon an error distribution of shootingerrors that the group is likely to make. The optimal target locationwithin the hoop that maximizes their chances of making the shot may bedifferent than the geometric center of the hoop. For instance, theoptimal target location may be closer to the geometric center of themake/miss zone, which tends to be deeper in the basket, i.e., behind thegeometric center of the hoop. In addition, if because of a player'sshooting habits or particular physique, i.e., such as being left handedor right handed, the player's tendency to make shooting errors is biasedin a particular direction, then a shooting strategy including a shootingtarget location can be developed that accounts for the particularshooting errors of the individual. These shooting errors may bedetermined from analysis of shot data gathered using the measuringdevices described with respect FIGS. 5-16.

FIG. 3A shows a prediction of shooting percentage as a function of thedistance from the front of the rim of the basketball hoop for abasketball rim with an 18 inch diameter. The prediction methodology isdescribed in more detail with respect to FIGS. 8-13. In FIG. 3A, theshooting percentage peaks at a distance of about 11 inches from thefront of the rim (the front of the rim is 0 inches), which is about twoinches behind the center of the hoop at 9 inches. FIGS. 3G and 3H showentry angle and rim location data gathered using embodiments of thedevices described herein for about 1000 players.

FIG. 3G shows a distribution of the average shot entry angle for the1000 players. As discussed herein, an optimum entry angle is about 43degrees. FIG. 3G illustrates that a large majority of players shoot ashot with a sub-optimal arc. FIG. 3H shows a location in the basketmeasure from the front of the rim as a function of the entry angle. Asdescribed above, 11 inches in the basket optimizes a predicted shootingpercentage. FIG. 3H illustrates that most players shoot shots withtrajectories that are not aimed at an optimal location within thebasketball rim. This data indicates a large majority of players couldbenefit from the training methodologies and devices described herein.

FIG. 4 shows top views of a backboard, basketball rim structure coupledto the backboard and net where a training aid is attached to the rim anda cross section of the training aid. A training aid can be devised thatencourages a shot target location that differs from the geometric centerof hoop. The training aid can extend around some portion of theperimeter of the hoop as shown in the figure. The distance that thetraining aid extends around the perimeter can be selected to allowtraining for shots other than straight on shots while also allowing forrim effects for long shots where the shot hits the back of the rim andgoes in. The training aid can be coupled to the rim and backboardstructure in some manner.

A possible triangular cross section for the training aid is shown in thefigure. The height of the triangle can be selected to encourage a playerto shoot deeper in the basketball, such as 2-3 inches behind thegeometric center of the hoop. Typically, the height of the training aidwill be less than 3 inches and possibly 2-2.5 inches above the topheight of the rim. The height of the training aid in some embodimentsmay be lower. For instance, cross-section of the training aid could bemore rectangular with the top of the training aid proximate to the topof the rim. The training aid can encourage players to shoot deeperbecause some shots that would normally be made will be deflected by thetraining aid.

As described with respect to FIG. 1C, shots that hit the rim and go incan be a large percentage of the made shots for a given entry angle. Forexample, as shown in FIG. 1C, shots that hit the back of the rim and goin, can compose a large fraction of the made shots for a particularentry angle. As shown in FIG. 1C, rim effects become more important atlower entry angles. Thus, In view of FIG. 1C, it may be desirable toconsider rim effects when designing a training aid that encourages aplayer to shoot deeper in the basket.

When a shot approaches the basketball hoop along a particulartrajectory, it can pass over the front of the rim and then interact withthe back of the rim. As described above, a training aid can be developedthat encourages a player to shoot deeper in the basketball by adding ahoop insert that blocks shots that just pass over the front the rimalong its trajectory within some margin to encourage shots deeper in thebasket. For instance, an insert can be designed that works forstraight-on shots, i.e., a shot vector that is perpendicular to thebackboard. This training aid can extend around some portion of the frontof the rim. Since the insert only extends around the front portion ofthe rim, the back of the rim is unaffected and rim effects can becorrectly reproduced.

To allow for non-straight on shots, the insert can be extended aroundperimeter of the rim. However, if the insert is extended too far, theinsert can interfere with rim effects related to the back part of therim associated with the shot vector. For instance, if the an insertextended around the front half of a basketball hoop, then for a shotfrom one side of the hoop, i.e., with a vector parallel to the backboard, the insert can block shots that just cleared the front rim, whichis desired, but can also block shots that would hit the back of the rimand go-in, which is not desired. In one embodiment, an insert can beprovided that covers about 90-110 degree arc of the rim, i.e, about onequadrant of the basketball hoop. The insert can extend from about orslightly past the front of the rim to one side of the rim to allow forstraight on shots as well as for shots from the side of the rim from oneside of the basket only.

In another embodiment, the rim insert could be placed on a track, suchthat its position can be rotated around the rim. If a motor is provided,this rotation can be provided through actuation of the motor. Else, therotation could be performed manually, such as by using a pole. As anexample, an insert that spanned proximately a quarter of the hoop couldbe rotatable from one side of the hoop to another side of the hoop. Toallow for shots from one side of the hoop, the insert would be rotatedto a first position. To allow for shots from opposite side of the hoop,the insert can be rotated to the opposite side of the hoop by sliding itaround the rim.

In yet another embodiment, if the insert can include parts that arerigid or flexible depending on the direction of the shot. For example,an insert can be configured that spans across the front-half of the rim.For a shot from one side of the basket, the part proximate to the frontof the rim can be rigid, while the part proximate to the back of the rimcan be flexible so as not to prevent the ball from hitting the back rimand going in. For a shot from the other side of the basket, the partthat was previously flexible can be designed to be rigid as it is nowthe front of the rim for this shot and the part that was previouslyrigid can be flexible as it now the back of the rim for this shot. Inone embodiment, the flexibility and rigidity of the insert can be variedusing sensors and mechanical actuators.

The training aid can be tailored to shooting errors associated with aparticular player, such that it encourages a shooting target locationthat is optimized for the shooting errors of an individual. As anexample, the training aid may be asymmetric around a line drawn betweena shot location and the center of the hoop to encourage a shot targetlocation that is left or right of this line for a straight on shot. Asdescribed above, this may be advantageous if the player shooting errorsare biased to the left or right of this line in some manner. Forinstance, for a player that tends to make more shooting errors to theleft as opposed to the right, the training aid may extend deeper intothe rim on left side of the hoop as opposed to the right to encouragethe player to target a shot location that is shifted to right of centerfor a straight on shot. Shooting slightly to the right of the center ofthe hoop may better accommodate the player's tendency to the make moreshooting errors to the left.

A trajectory capture and feedback system, as is described in thefollowing figures, can also be used to help a player train to shoot to atarget location in the hoop that differs from the geometric center ofthe hoop. This system could be used a training device as described withrespect to FIG. 5 or separately from the training device. The feedbackinformation could be provided relative to a selected target locationwithin the hoop, such as ‘short or long,’ left or right' or combinationsthereof. The feedback information could also be combined with othertrajectory information, such as entry angle feedback. For instance,combination feedback could include short 43 or long 43 to indicate theentry angle was 43 degrees but the shot entered the basket short or longof the target location.

FIG. 5 is a diagram of a trajectory capture and feedback scenarioemploying a trajectory detection and feedback system of the presentinvention. In the embodiment shown in the figure, a trajectorydetection, analysis and feedback system 100 uses a machine vision systemwith a single camera 118 to detect and to analyze a trajectory 102 of abasketball 109 shot towards the basketball hoop 103 by the shooter 112.The camera 118 may record visible light.

The basketball hoop 103 may be mounted to a backboard 151 with a supportsystem to hold it up, such as a pole anchored into the ground, a supportanchored into a wall or supports suspended from a ceiling. Thebasketball hoop 103 may be of a standard height and the basketball maybe a standard men's size basketball. However, trajectories for abasketball of a different size, such as a women's ball, shot atbasketball hoop of varying heights may also be detected and analyzedwith the present invention.

The camera 118 in the machine vision system records physical informationwithin a detection volume 110. The physical information that is recordedis images of objects at a particular time in the detection volume 110.The images recorded at a particular time may be stored as a video frame106. The camera 118 may capture images of the basketball 109 as it movesin trajectory plane 104 as well as images of other secondary objects.The secondary objects may be closer to the camera than the basketball109 (i.e., between the camera 118 and the trajectory plane 104) or thesecondary objects may be farther away from the camera than thebasketball 109 (i.e., beyond the trajectory plane 104). The machinevision system may utilize software to distinguish between the movementof secondary objects that may be detected and the movement of thebasketball 109.

The trajectory detection system 100 may be set-up in a playing areawhere basketball is normally played, such as a basketball court withplaying surface 119 located in gymnasium or arena. The system 100 may bepositioned on the side of court and remotely detect the trajectories ofthe shots by shooter 112 using the machine vision system. Thus, theshooter 112 and defender 114 may engage in any of their normalactivities on the playing surface 119 without any interference from thedetection system 100. In the figure, the shooter 112 is guarded by adefender 114. However, the system 100 may also be used when the shooter112 is unguarded.

With a machine vision system that uses a single camera 118, thelocations where the trajectory 102 may be accurately analyzed may belimited. In one embodiment, with the set-up of the trajectory detectionsystem 100 on the side of playing surface 119, accurate analysis mayrequire that the shooter 112 shoot from within the active area 108. Inthis alignment, the trajectory plane 104 may be nearly normal to thebasketball backboard 151. Although, the system 100 may accurately detectand analyze trajectories where the angle between the trajectory plane104 and the normal to the backboard 151 is within a few degrees. Theactive area 108 may be different for different systems 100. Further, thepresent invention is not limited to machine vision systems for detectingthe trajectory of the basketball and other sensor systems may allow fordifferent active areas.

The trajectory system 100 may be set-up in different locations aroundthe playing surface 119. By moving the system 100, the active area 108may be changed. For instance, the trajectory detection may be positionedbehind the backboard 151. For this set-up, the active area 108 may be arectangular area on the playing surface 119 that is parallel to thebackboard 151.

Although the active area 108 may be limited with a single camera 118 ina machine vision system, an advantage of the system is it simple toset-up and to operate. With some multiple camera machine vision systems,the active area may be larger than with a single camera system. However,the set-up and calibration of a multi-camera system may be more timeconsuming as compared to a single camera system because a knownalignment of the cameras relatively to one another and relative to thetracked object is needed to process the data.

The single camera system 100 is simple enough to be capable ofautonomous set-up and operation with minimal user input. The system mayautonomously calibrate itself using known distance markers, such as theheight of the basketball hoop or a distance to a free throw line or3-point arc, which may be captured in video frame data. In anotherembodiment, a user may be required to stand within the detection zone ofthe system, holding a basketball or other object, at a fixed distancefrom the camera and at a fixed height. After the system is calibrated, auser may use the system 100 to practice without the help of anadditional operator to run to the system 100. The system 100 may acceptvoice commands allowing the user to adjust the operation of the systemfrom a distance.

To analyze a trajectory 102 of the basketball 109, the camera 118 mayrecord a sequence of video frames in the detection volume 110 atdifferent times. The number of frames recorded by the camera over a givetime period, such as the duration of the ball's trajectory 102, may varyaccording to the refresh rate of camera 118. The captured video framesmay show a sequence of states of the basketball 109 at different timesalong its trajectory 102. For instance, the camera 118 may capture 1) aninitial state 105 of the trajectory shortly after the ball leaves theshooter's hand, 2) a number of states along the trajectory 102, such as120, 121, 122 and 123 at times t1, t2, t3 and t4 and 3) a terminationpoint 107 in the basketball hoop 103. Although not shown, the system mayalso be used to generate parameters for characterizing the trajectory ofmissed shots relating to the rebound flight path, such as but notlimited to a rebound height, rebound angle, rebound velocity.

The sequence of captured video frames may be converted to digital databy a video capture card for analysis by the CPU 116. The analysis ofvideo frame data may require the detection volume 110 to remain constantduring the trajectory 102. However, the detection volume 110 may beadjusted to account for different set-up conditions of a playing areawhere the system 100 is employed. For instance, the camera 118 may becapable of zooming in or out of a particular area and changing itsfocus.

The series of frames used to capture the trajectory may also capture theshooter 112 shooting the basketball 109 including all or a portion ofthe shooter's 112 body as well as the defender's body 114 during theshot. The physical information captured by the camera 118 regarding theshooter 112 and the defender 114 may also be analyzed by the system 100.For example, different motions of the shooter 112 may be analyzed by thesystem 100 determine if the shooter is using proper shooting mechanics.As another example, data, such as, a jump height, hang-time, a releasepoint floor position on the playing surface 109, a landing position onthe playing surface 109 may be determined using the video frame datacaptured by the camera 118 in the machine vision system.

After detecting and analyzing the trajectory 102, the system 100 maygenerate one or more trajectory parameters. The one or more trajectoryparameters may be output as feedback information to the shooter 112 andthe defender 114. Typically, the system 100 may provide the feedbackinformation while the shot is in the air or shortly after the shot hasreached the hoop 103. The feedback information may be provided withinless than a second or less than 10 seconds of the initiation of the shotdepending on the type of feedback information that is generated. Theimmediate feedback may increase the training benefits of using thesystem. The shooter 112 may use the feedback information to improvetheir skill at making shots. The defender 114 may use the feedbackinformation to improve their defense in preventing the shooter frommaking their shots. A brief description of the methods used to developthe feedback information is described as follows.

The shooter 112 may also use the feedback information for rehabilitativepurposes. For instance, after an injury and/or for psychologicallyreasons, a player's skill at shooting may decline from a previouslyobtained skill level. In rehabilitative setting, the present inventionmay be used by the player to regain their previous skill level and evenimprove upon their previous skill level. For instance, the feedbackinformation provided by the present invention may increase a shooter'sconfidence which may provide psychological benefits that lead to animprovement in performance.

To develop basketball feedback information, the basic nature of abasketball shot is considered with the objectives of 1) informing theplayer in regards to what are a set of optimal trajectory parametersthat they can adjust to increase their probability of making a shot and2) informing their player about how their shots compare to the optimal.This information is output to the player as feedback information. As anexample of this process, the basketball shot by the shooter 112 isdescribed. However, the system 100 may be applied to the trajectories ofother objects in different sports where optimal trajectory parametersmay be different than basketball. Thus, the description is presented forillustrated purposes only.

The basketball shot by the shooter 112 travels in an essentiallyparabolic arc in the trajectory plane 104. The arc is essentiallyparabolic and the ball 109 travels in-plane because after the ball isreleased the dominant force acting on the ball is gravity 109. Otherforces, such as ball spin, or if the ball is shot outside, wind, maycause the trajectory to deviate from a parabolic arc. But, when the ballis shot inside, these forces cause little deviation from the parabolictrajectory and a parabolic arc is a good approximation of the trajectory102.

For each shot by the shooter with an initial release height, there aremany different combinations of release velocity and release angles atthe initial state 105 that allow the player to make the shot, i.e., theball travels through the basket 103 and then many combinations ofrelease velocity and release angles where the player does not make theshot. When a player shoots the basketball 109, the player selects acombination of release velocity and release angle. Typically, theselection of the shot parameters is performed intuitively and the playerdoesn't consciously think of what release velocity and release anglethey are selecting. However, through training, the player may be able toimprove their intuitive shot selection.

Within the group of the different combinations of release velocity andrelease angle that may be selected by the shooter, there arecombinations of release velocity and release angle that provide theshooter with a greater or lesser margin of error for making the shot.For instance, for a basketball shot in the basket 103, an optimal entryangle into the hoop that provides the greatest margin of error is about43-45 degrees measured from a plane including the basketball hoop 103.These optimal trajectories are close to trajectories that allow for theball to reach to the basket 103 with a minimal amount of energy appliedby the shooter. For perturbations around this optimal entry angle, suchas when the defender 114 causes the shooter 112 to alter their shot,there are more combinations of release velocity and release angle thatallow the shot to be made as compared to other combinations of releasevelocity and release angle away from the optimal.

With the general understanding of basketball trajectories providedabove, methods may be developed for providing feedback information thatallows for the shooter 112 to train for an initial state 105 thatprovides the greatest margin of energy i.e., a near minimum energytrajectory. In one embodiment of the present invention, an entry angleand an entry velocity of the basketball 109 near the termination point107 are two trajectory parameters that may generated from the physicalinformation recorded by the machine vision system in system 100. Theentry angle and entry velocity are correlated to the release angle andthe release velocity of the shot 102. Thus, after the shooter 112,releases the shot, the camera 118 may record a series of video frameswith images of the ball 109 as it approaches the basket 103. With thisinformation, the entry angle and the entry velocity of the shot may begenerated. One or both of these trajectory parameters may be provided tothe player as feedback information.

The feedback information may be provided to the shooter 112 and thedefender 114 in one of a visual format, an audio format and a kineticformat. For instance, in one embodiment, on a visual display, the entryangle and/or entry velocity may be viewed in a numeric format by theplayers, 112 and 114. In another embodiment, when projected through anaudio device, numeric values for these parameters may be heard by theplayers, 112 and 114. The audio feedback device may be a speaker builtinto the system 100, a speaker connected to the system 100 or audiodevices worn by the players, 112 and 114 that receive information fromthe system 100. In yet another embodiment, a kinetic device, such as abracelet or headband worn by the players may be used to transmit thefeedback information in a kinetic format. For instance, the bracelet mayvibrate more or less depending on how close the shot is to the optimumor may get hotter or colder depending on how close the shot is theoptimum. Multiple feedback output mechanisms may also be employed. Forinstance, the feedback information may be viewed in a visual format bycoaches or other spectators on a display while a sound projection devicemay be used to transmit the feedback information in an audio format tothe players.

In general, the parameters may be presented qualitatively orquantitatively. An example of qualitative feedback may be a message suchas “too high” or “too low” in reference to the entry angle of a shot bythe player or “too fast” or “too slow” in reference to the entryvelocity. An example of qualitative feedback may be the actual entryangle or entry velocity of the shot in an appropriate unit ofmeasurement, such as a message of “45 degrees” for the entry angle.Again, the qualitative and/or quantitative information may be presentedin different formats, such as a visual format, an auditory format, akinetic format and combinations thereof.

With knowledge of what are optimal values of the trajectory parameterstransmitted in the feedback information, the shooter 112 may adjusttheir next shot to generate a more optimal trajectory. For instance, ifthe feedback information is an entry angle and their shot is too flat,then the shooter 112 may adjust their next shot to increase their entryangle. Conversely, with their knowledge of what are the optimal valuesof the trajectory parameters, the defender 114 may adjust theirdefensive techniques to force the shooter 112 to launch a shot along aless than optimal trajectory 102. Thus, the defender 114 can experimentwith different techniques to see which are most effective. In differenttraining methods, the system 100 may be used to measure a trajectoriesfor a shooter 112 training without a defender 114 or as is shown in thefigure training with the presence of a defender 114.

The feedback information may be provided to the player before prior tothe ball 109 reaching the basket or shortly after the ball reaches thebasket 103. The system 100 is designed to minimize any waiting timebetween shots. For each shooter and for different training exercises,there may be an optimal time between when the shooter shoots the ball109 and when the shooter 112 receives the feedback information. Thesystem 100 may be designed to allow a variable delay time between theshot and the feedback information to suit the preferences of eachshooter that uses the system 100 or to account for different trainingexercises that may be performed with the system. For instance, a rapidshooting drill may require a faster feedback time than a more relaxeddrill, such as a player shooting free throws.

The present invention is not limited to providing feedback informationfor near minimum energy basketball trajectories. For instance, undersome conditions, such as when a smaller player shoots over a largerplayer, it may be desirable for the shooter to shoot with a greater thanoptimal arc to prevent the larger player from blocking the shot. Thus,the shooter may use the feedback information provided by the system 100to train for different conditions that may call for different types ofshots, such as shooting over a larger player as compared to a wide-openshot. Further, the trajectory analysis systems of the present inventionmay be used to train in different types of basketball shots, such asbank shots, hook shots, lay-ups, jump shots, set-shots, free throws andrunning shots, that may requiring the mastery of different shootingskills and may have different optimal trajectory parameters. Thus, thedetection system 100 may be adjustable to allow for training indifferent types of shots. Further, for different sports, differenttrajectory skills may be optimal for improving performance, which may bedifferent than basketball. The different trajectory skills that may berequired for different sports may be accounted for in the presentinvention.

A measure of how good a player's shooting skills may be a consistency oftheir trajectory parameters averaged in some manner over many shots.Typically, it has been determined empirically that better shooters havea lower variability in their trajectory parameters for a given shot,such as a free throw. Thus, to rate a shooter's performance, it may bedesirable to generate trajectory parameters for a plurality oftrajectories shot by a player in a trajectory session and then calculatea standard deviation for each of the trajectory parameters.

The standard deviation (SD) is a measure of the scatter of a particularset of data. It is calculated as,

SD=[3(yi−y _(mean))²/(N−1)]^(1/2)

where y_(mean) is an average value of trajectory parameter, N is thenumber of trajectories and yi is a value of the trajectory parameter fora particular trajectory. There are other types of statistical parametersthat may be used to characterize data variability and the presentinvention is not limited to the standard deviation formula describedabove.

During a trajectory session where a plurality of trajectories areanalyzed by the system 100, the trajectory parameters generated for theplurality of trajectories may be stored to a mass storage devicecontained in the system 100 or in communication with the system 100.After the session, the standard deviation for all the trajectories inthe session may be generated. In other embodiments, to provide measuresof variability of different data sets representing different playingconditions, the system 100 may divide the trajectory data into differentsubsets, such as grouping according to types of shots, locations ofshots, shots where the shooter is guarded, shots where the shooter isunguarded, made shots, swished shots, missed shots, shots made earlierin the session versus shots made later in the session, and combinationsof these groupings.

The statistical variability calculated from the different data sets maybe used as a guide by the system for suggesting methods that willimprove the player's shooting skills. The system 100 may includesoftware for suggesting methods based upon the statistical analysis. Forinstance, the system 100 may determine that a player's shot variabilityis greater when they are guarded as opposed to unguarded, thus,exercises may be prescribed to the player that focus and shooting whileguarded. As another example, the player's shot variability may begreater later in a session as opposed to earlier in a session or greaterin a training session before practice as opposed to after practice,thus, the system may suggest the player work on their aerobicconditioning. In yet another example, the player's shot variability mayvary as a function of a distance from the basket and the system maysuggest the player concentrate on shots at the distances where thevariability is greatest.

In some embodiments, the trajectory session data and other informationgenerated by the system 100 may be viewed via a number of differentoutput mechanisms, such as a hard copy from a printer or a display. Forexample, a printer connected to the system 100 may be used to generateprint-outs of trajectory session data in different formats. As anotherexample, a display interface in communication with the system 100 may beused to view trajectory session data in different formats. Inparticular, the system 100 may include a touch screen interface forviewing trajectory session data and providing input parameters into thesystem. As another example, the system 100 may communicate with aportable viewing device capable of interfacing with the system 100.

Information generated with system 100, such as trajectory data from aplurality of trajectories in a trajectory sessions, may be archived. Thearchival storage system may be a remote storage device in communicationwith the system 100 or may be a mass storage device provided with thesystem 100. The archival storage system may include raw data of physicalinformation recorded by the camera 118, such as video frame data, aswell as, trajectory parameters and other information generated fromanalysis of the raw data. The archival data may store trajectory sessiondata for a plurality of different trajectory sessions by one or moredifferent players.

By accessing the archival data, an improvement over time for aparticular parameter generated by the system 100, such as a shotvariability parameter, may be assessed. Further, the archival data maybe used for data mining and video editing purposes. For instance, in avideo editing application, the graphic of the player's averagetrajectory may be integrated with video data of the player shooting. Inanother example, video clips of two or more different players shootingmay be compared or video clips of a single player shooting duringdifferent trajectory sessions may be compared to show the player'simprovement. In data mining applications, the video data may be furtheranalyzed to characterize a player's shot mechanics. In anotherapplication, simulations may be generated to predict gains in teamperformance based-upon improvements in individual performance on theteam. This type of simulation may require archival trajectory sessiondata to be analyzed for a plurality of different players.

In some embodiments, the archival data may be accessible via a remoteconnection. For instance, a password-protected web-site may be used as aportal for accessing archival data generated from system 100. Theweb-site may allow clients, such as players, coaches, or scouts to gainaccess to the web-site from remote sites, such as home computerconnected to the Internet or a portable computer connected to theInternet. The web-site may include a plurality of analysis tools and agraphical interface for viewing graphical data from the applications indifferent formats. In another embodiment, the archival data may bedownloaded to a CD, DVD or other portable storage medium that the playercan take with them. Analysis software may also be downloaded with thearchival data so that the player can analyze the data on anothercomputer.

Information generated during a trajectory session may be stored in adatabase. The database may relate player identification information,such as a name, an address, a team, a session time, a session location,a session data to raw data recorded during the trajectory session andinformation generated during the trajectory session. The database may beused for player tracking purposes and targeting services to players thathave used the trajectory system.

FIG. 6 is a diagram of trajectory capture scenario employing variousembodiments of a trajectory detection and feedback system. In oneembodiment, a portion of the feedback system, such as 100 a, can be wallmounted for a more permanent installation. For example, a wall mountedsystem could include a machine vision system using camera 118 to providetrajectory analysis. The system 100 a could include a CPU 116 that canbe used in image processing. Further, the system 100 a could include aspeaker for providing feedback information to a user. In general, thesystem 100 a can be designed for more permanent installation, such as ona wall, a pole separate from the basketball hoop structure or attachedto the basketball hoop structure.

When the device is turned on, it may be configured to begin providingfeedback information until it is turned off. The device may include awireless or wired remote to provide options, such as but not limited tochanging the feedback format options, recalibrating or resetting thedevice, changing the volume of a speaker or turning the device on oroff. In one embodiment, the device may include a limited memory that canbe overwritten over time. The memory may include captured images and/orassociated trajectory analysis. For instance, the memory can be sized tostore 24 hours of video that includes a time stamp. After the 24 hoursof video are filled, the device can begin to rewrite over the oldeststored video with new captured video data.

The device 100 a may include a wired and/or wireless interface thatallows stored data including image data to be downloaded to a separatedevice, such as but not limited laptop computer or a cell phone. Forinstance, image data could be downloaded over a particular time periodas selected by a user and downloaded to their device. The device 100 amay provide video indexing and skipping features that allow a user tolocate video data stored on the device and review it on their device.For instance, a preview capability could be provided that is compatiblewith a user's cell phone, such that the video stored on the device 100 acould be viewed on a screen associated with the user's cell phone.Software downloads could be provided from the device 100 a or fromanother remote location, such as server associated with a website, thatallows captured image data downloaded from the device 100 a to befurther manipulated and stored on the user's device, such as theircellphone or laptop. In another embodiment, a web-site may be set upthat allows data stored on their personal device, such as a cell phoneor laptop, to be uploaded an further processed using software providedin association with the web-site

In other embodiments, a server associated with a web-site, may beconfigured to download software to a user's device with a camera thatallows it to behave like the machine vision system described withrespect to FIGS. 5 and 6. For instance, the web-site could provide anapplication that allows an iphone from Apple™ that is available at anapp store that allows iphone to act as an image capture and analysissystem. As another example, an application could be downloaded to auser's laptop, camera or camcorder that allows these devices to functionin this manner.

Thus, when one of these devices where placed near a sports venue, suchas indoor or outdoor basket ball hoop structure, the device could beused to provide image capture and trajectory analysis capabilities. Ifthe device included audio capabilities, it could also be used to providefeedback information. For instance, a cell phone could be configured tocommunicate with a Blue-Tooth™ capable head set worn by a user andcoupled to the cell phone to provide feedback information. In anotherembodiment, a portable speaker system could be coupled to the cell phoneto provide audio capabilities.

In one embodiment, a docking station or stand, such as a tripod, couldbe provided for use with a user's device, such as a cell phone, cameraor camcorder. The docking station could be configured to allow a user'sdevice to be fixed in a particular orientation. For instance, thedocking station or stand could include a flexible device that attachesto the cellphone or camera that allows it to be mounted in variousorientations, such as a multi-armed Gorrilapod.™ The docking station mayalso be configured to allow augment features of the user's device. Forinstance, the docking station could include a power source, apower/communication interface, such as a USB compatible interface,additional electronic storage and additional processing.

The docking station could also be designed with an enclosure thatprovides some protection to the device. For instance, the enclosurecould cover the device to provide some protection from rain. Further,the enclosure could partially enclose and secure the user's device toprotect it from damage if it were impacted in some way, such as hit byan errant basketball or other object for which the device is being usedto capture and analyze trajectory data.

Calculating Basketball Trajectory Dynamics: Basketball Swish/MakeAnalysis

When a basketball shot goes through the hoop without contacting any partof the rim, we call it a “swish.” Since the hoop is larger than theball, there can be some variation in the shot and still get a swish.This analysis first determines the range of straight-on shots that willswish. The shot possibilities may be described by locating the center ofthe ball at the instant it passes through the hoop or, more technically,when the center of the ball lies in the plane of the hoop. The locus ofpoints that describe shots that swish may be referred to as the swishzone, and can be illustrated by drawing a top view of the hoop with theswish zone defined within that circular region. The reference point(coordinate system origin) is the center of the hoop, with the positivex-axis projecting to the right and the positive y-axis projecting towardthe back of the hoop, as shown in FIG. 7A.

For the purposes of illustration, it may be assumed that the hoop is 9″in radius and the ball is a men's pro ball, approximately 4.77″ inradius. These assumptions may be varied to address different hoop andball geometries as desired. For this example, it may be assumed that theball's trajectory is a straight line in the immediate vicinity of thehoop, described by the hoop entry angle and measured from thehorizontal. In this frame of reference, a perfectly flat shot would be 0degrees and a ball dropped from directly above the hoop would be 90degrees. This analysis may be generalized to include a morerepresentative parabolic trajectory, or even a trajectory corrected foraerodynamic and buoyant forces, if necessary. For this example, it maybe assumed the curvature of the trajectory in the immediate vicinity ofthe hoop is insignificant.

For the ball to swish, it must pass over the front of the rim and underthe back of the rim. These constraints limit the range of possible shotsthat may swish for a given entry angle, and the widest part of the ball(its diameter) determines the extent of that range. The geometry may bedescribed for the longest possible swish at a particular entry angle andshortest possible swish at a particular entry angle. FIG. 7B is a sideview of basketball shot passing through hoop at location of longestpossible swish and FIG. 7C is a side view of basketball shot passingthrough hoop at location of shortest possible swish.

As can be seen in FIG. 7B, the center of the ball is below the rim whenthe widest part of the ball passes the rim for the longest possibleswish. This is because the radius of the ball is measured perpendicularto the flight path in order to ensure the ball is a sufficient distanceaway from the rim to pass without hitting it. Similarly, for theshortest possible swish, the center of the ball is above the hoop whenthe widest part of the ball passes the rim, as shown in FIG. 7C. Inorder to define the range of swish shots for a given entry angle, thelocation of the center of the ball must be projected onto the plane ofthe hoop. This is accomplished by simple trigonometric computation usingthe expression

y=R _(hoop) −R _(ball)/sin(θ)

wherey=location of center of ball in plane of hoopR_(hoop)=radius of basketball hoop (set at 9″)R_(ball)=radius of basketball (set at 4.77″)θ=shot entry angle measured from horizontal

This formula results in the following values for the longest andshortest possible swish shots as a function of shot entry angle:

Angle Y long Y short 90 4.23 −4.23 89 4.229273 −4.22927 88 4.227092−4.22709 87 4.223454 −4.22345 86 4.218352 −4.21835 85 4.211779 −4.2117884 4.203726 −4.20373 83 4.194178 −4.19418 82 4.183122 −4.18312 814.170541 −4.17054 80 4.156415 −4.15642 79 4.140721 −4.14072 78 4.123435−4.12344 77 4.104529 −4.10453 76 4.083973 −4.08397 75 4.061733 −4.0617374 4.037772 −4.03777 73 4.01205 −4.01205 72 3.984525 −3.98453 713.955149 −3.95515 70 3.923872 −3.92387 69 3.890638 −3.89064 68 3.855389−3.85539 67 3.818061 −3.81806 66 3.778585 −3.77858 65 3.736887 −3.7368964 3.692889 −3.69289 63 3.646504 −3.6465 62 3.597641 −3.59764 613.546201 −3.5462 60 3.492078 −3.49208 59 3.435159 −3.43516 58 3.375319−3.37532 57 3.312427 −3.31243 56 3.24634 −3.24634 55 3.176905 −3.1769154 3.103956 −3.10396 53 3.027313 −3.02731 52 2.946783 −2.94678 512.862157 −2.86216 50 2.773207 −2.77321 49 2.679688 −2.67969 48 2.581332−2.58133 47 2.477848 −2.47785 46 2.36892 −2.36892 45 2.254201 −2.2542 442.133315 −2.13332 43 2.005848 −2.00585 42 1.871347 −1.87135 41 1.729313−1.72931 40 1.579197 −1.5792 39 1.420395 −1.42039 38 1.252236 −1.2522437 1.073977 −1.07398 36 0.884791 −0.88479 35 0.683759 −0.68376 340.469849 −0.46985 33 0.241906 −0.24191 32 0 0

These results apply to a straight-on shot. In order to calculate theswish zone for off-center shots, compound angles must be computed thatare difficult to illustrate geometrically. The result is more easilydepicted graphically by showing the swish zone within the hoop. Forexample, the swish zone for a 45-degree shot is shown in FIG. 8.

Make Zone

It is still possible for the ball to go through the hoop if it does notpass through the swish zone. Shots near the swish zone will hit the rim.Depending on the shot and hoop geometry, it is possible for the ball tobounce off the rim and pass downward through the hoop. The locus ofpoints for which this occurs may be called the make zone. The boundaryof the make zone may be defined by the longest shot that can hit theback rim and rebound downward to the plane of the hoop before contactingthe front rim. FIG. 9 is an illustration of the geometry of rim-in shotoff the back rim.

The location of the boundary of the make zone for a straight-on shot maybe determined from the following system of equations, which are shown inFIG. 9.

h=√r _(b) ²−(r _(h) −y ₁)²

β=sin⁻¹(h/r _(b))

γ=θ−β

γ=tan⁻¹(h/(r _(h) −r _(b) +y ₁))

whereh=height of center of ball above plane of hoop when ball strikes backrimr_(b)=radius of ballr_(h)=radius of hoopy₁=y-location of center of ball in plane of hoop when ball strikes backrimβ=angle between rim-normal and plane of hoopγ=angle between plane of hoop and resultant ball direction afterrebounding off back rim

These equations do not have a closed-form solution. Nevertheless, theequations may be solved iteratively using a variety of progressivesolution techniques, such as the Newtonian method. Using this method,the location of the make zone boundary may be determined as a functionof entry angle. The results of a sample calculation are given in thetable below.

Entry angle, deg. Make zone boundary, in. 50 5.04 45 4.88 40 4.73 354.61 30 4.51 25 4.42 20 —

The table indicates that below 25 degrees entry angle, there is no makezone. The geometry for off-center rim shots is more complicated, but themake zones may be depicted graphically. There are some idealizationsused in generating these plots that may be relaxed if necessary toproduce a more accurate depiction of the make zone.

FIG. 10A is a plot of a make zone for a hoop entry angle of 45 degrees.Three curves are depicted in a circle, which depicts the hoop. The areabetween the dashed lines represents the swish zone. The area between theupper solid line the lower dashed line represents the make zone. FIG.10B is a plot of the make zone for a hoop entry angle of 25 degrees.Again, three curves are depicted in a circle. There is no swish zone atthis entry angle. This is indicated by the dashed curves in the figurewhere the lower dashed curve and upper dashed curves depicted in FIG.10A have switched positions in FIG. 10B. The make zone in FIG. 10B isdefined by the area between the solid downward turned curve and theupwardly turned dashed curve depicted in the figure.

In performing this analysis, a conservative assumption has been madethat only rim bounces that cause the ball to continue downward have thepotential to score. In practice, many shots are observed to bounce upoff the rim, then either drop through the hoop or make subsequentcontact with the rim and/or backboard ultimately resulting in a madeshot. As a result, the make percentage calculated by the present methodmay be lower than what would be expected in practice. This observationhas been confirmed with empirical data as is described with respect toFIGS. 11 and 12.

One means of addressing this under-prediction of made shots may be todevelop a calibration factor based on empirical evidence. The make zonemay be enlarged by a multiplicative factor such that the calculated madeshots more nearly replicate observations. This factor, which may bedependent on a number of variables such as entry angle and speed, may bededuced from an experimental dataset, then applied to the algorithm foruse in subsequent predictions.

Another approach to developing a more accurate make zone may be toincorporate a more complete kinetic model of the ball and itsinteractions with the hoop, bracket, and backboard. Effects to beincluded may include the angle of rebound when the ball contacts a solidsurface, the effects of spin and ball friction against a solid surface,energy loss of the ball as a result of its impact, and the flexibilityand energy absorption of the hoop and associated hardware. This wouldallow the calculation to model multiple ball/rim interactions andthereby determine the make zone even for very complex dynamics. Thebounce dynamics may also be verified experimentally.

A rear view of an experimental set-up for generating basketballtrajectories is shown with respect to FIG. 11. The shooting machine 1302includes an arm 1308 that can launch a basketball 1306 (a realbasketball is not shown in the figure only an outline of a basketball isshown) towards a basketball hoop 1300 along a trajectory 1304. The armis propelled by mechanism 1310. The shooting machine 1302 includes anon-off switch and a display/control mechanism 1312.

The machine 1302 may be programmed to execute a large number of shotsand the outcome for each shot may be recorded. The release height of thedevice may be set to a particular value. From shot to shot, a left-rightorientation of the shot relative to the center of the basketball hoop, arelease velocity and a release angle may be automatically adjusted. Eachof the values, left-right orientation, release velocity and releaseangle may be varied to generate a number of shots, such as but notlimited to 10,000 shots. Different ball sizes may be employed with themachine 1302, such as a men's ball or a women's ball.

The shooting machine may be positioned at a location on the court 1314that is a fixed distance from the basketball hoop. In this example, theshooting machine 1302 is positioned to generate a shot near the freethrow line. The shooting machine is mobile and may be moved to differentlocations to generate a set of shots at each location.

FIG. 12 is a plot of a theoretical make percentage predicting fromanalytical method previously described as compared to an actual makepercentage generated using the shooting machine described with respectto FIG. 11. The shooting machine was positioned to generate a free throwshot at a release height of 9 feet using a men's ball. The range ofparameters used to perform both the theoretical calculations and theactual shots generated using the shooting machine were selected to matcha variability of a particular individual. The variability and theassociated range of parameters was determined from a number of shotsactually made by the individual

From an entry angle between 40-65%, the theoretical make/miss percentageis 2-3 percentage points less than the experimentally predicted values.Below 40%, the error between the calculations is greater. As previously,mentioned some rebound dynamics were not considered in the theoreticalcalculations for the embodiments described herein and hence some shotsthat may be made are not captured by the methodology, such as hittingthe back rim, then the front rim and then going in. At lower entryangles, shots such as these are more prevalent as compared to the higherentry angles and hence there is a larger error in the calculations atlower entry angles.

As previously noted, it may be possible to better model the rim effectsand hence produce a more accurate simulation. In another embodiment, itmay be possible to correct the theoretical simulation using a correctionfactor derived from the shooting machine data. In yet anotherembodiment, it may be possible to generate a series of curves like theone shown in FIG. 12. The curves may be generated based upon datagenerated using the shooting machine, data generated from theoreticalcalculations, alone or in combination. Next, based on a measuredvariability of a particular individual, an existing curve that isappropriate for the variability of the individual may be located or acurve may be interpolated or extrapolated from existing curves asneeded. Thus, it may not be necessary to perform additional trajectorysimulations to determine an optimal or maximum shooting percentage forthe individual in the manner shown in FIG. 11.

Of note in FIG. 12, an optimum shooting angle is predicted for theindividual based upon their measured variability in their shootingmechanics (i.e., body motion and body orientation). The theoretical andexperimental data both predict an optimum entry to be about 45 degrees.In this example, the shooter had a variability that was characteristicof a highly skilled shooter. Thus, a recommendation for this type ofplayer may be to adjust their shot so that their average entry angle isa close to 45 degrees as possible.

FIG. 13 shows standard deviations for launch angle and launch velocityas a function of entry angle for a number of experimentally generatedshots and a percentage of shots made for various entry angles. Two shotstypes of shots are plotted: 1) shots that pass through the rim withouttouching the rim and 2) shots that hit the back of the rim and gothrough the rim. It can be seen in the figure that as the entry angleincreases, the percentage of swish shots increases. The percentage ofshots made is greatest for the 45 degree entry angle.

FIG. 14 is a block diagram of a trajectory detection and analysis system100 for one embodiment. The components of the system 100 may be enclosedwithin a single housing or may be divided between a plurality ofdifferent housings enclosing different components of the system.Further, the system 100 may include different components that are notshown, such as the peripheral devices and remote servers.

Physical information 216 is input into the system 100 via sensors 212.In one embodiment, a machine vision system may be used where the machinevision system comprises one or more cameras 201 (e.g., a CCD camera) anda video capture card 203 for digitizing captured frame data. The videocapture card 203 may capture color pixel data. The camera 201 may employa 3.5-8 mm zoom lens and may allow for different lens attachments. Inanother embodiment, the system may employ a plurality of camerasarranged on a mechanism that allows different type cameras to be rotatedor moved into place where only one camera is used at a time to recordframe data. The different cameras may allow the detection volume of thesystem to be adjusted.

The digitized frame data from a machine vision system and other sensordata may be processed by a computer 202. The computer 202 may be amodified PC using a 1.6 GHz processor 204 w/RAM and a CD-RW drive 205for inputting and outputting data and software. The computer 202 mayalso include a mass storage device, such as hard drive 207 and variousnetwork/device communication interfaces, such as wireless and wirednetwork interfaces, for connecting to a local area network (LAN),wide-area network (WAN) or the Internet. The device communicationinterfaces may allow the computer to communicate with a plurality ofperipheral devices and other remote system components.

The computer 202 may include operating system software 206 forcontrolling system resources, such as feedback interfaces 213 and thesystem input/output mechanisms 215. The computer 202 may be used toexecute analysis software 208 for analyzing trajectories using thesensor data from sensors 212 and for generating feedback information217. The analysis software 208 may include software for providingvarious services, such as 1) providing a list or a plot of trajectorysession information comprising one or more of physical information,trajectory parameters and feedback information for the plurality oftrajectories, 2) comparing the trajectory session information from thetrajectory session with trajectory session information from one or moredifferent trajectory sessions, 3) generating trajectory sessionparameters used to characterize a human's performance in the trajectorysession, 4) predicting performance improvement as a function of thetrajectory session parameters, 5) prescribing actions for improvingperformance and 6) performing video editing tasks. The computer 202 mayalso be used to execute database software for relating physicalinformation 216 and other information generated by the computer 202 toplayer identification information (e.g., name, age, address, team,school, etc.) and session identification information (e.g., time, data,location, number of trajectories analyzed, types of shots, etc.).

Power to the computer 202 and other devices may be provided from thepower supply 209. In one embodiment, the power supply 209 may be are-chargeable battery or a fuel cell. The power supply 209 may includeone or more power interfaces for receiving power from an externalsource, such as an AC outlet, conditioning the power for use by thevarious system components. In one embodiment, for in-door/outdoormodels, the system 100 may include photocells that are used to providedirect power and charge an internal battery.

Feedback information 217, used by clients of the system 100 to improvetheir trajectory skills, may be output through one or more feedbackinterface devices 213, such as a sound projection device 211. Ingeneral, the system may be capable of outputting feedback information217 to a plurality of different devices simultaneously in a plurality ofdifferent formats, such as visual formats, auditory formats and kineticformats.

The system 100 may support a plurality of different input/outputmechanisms 215 that are used to input/display operational information218 for the system 100. The operational information 218 may includecalibration and configuration setting inputs for the system and systemcomponents. In one embodiment, a touch screen display 210 may be used toinput and display operational information 218 using a plurality ofmenus. Menus may be available for configuring and setting up the system100, for allowing a player to sign into the system and to selectpreferred setting for the system 100 and for viewing session information219 in various formats that have been generated by the system. Theprinter 214 may be used to output hard copies of the session information219 for a player or other client of the system 100. The presentinvention is not limited to a touch screen display as an interface foroperational information. Other input mechanisms, such as but notlimited, a key board, a mouse, a touch pad, a joystick and a microphonewith voice recognition software may be used to input operationinformation 218 into the system.

FIGS. 15A-15C are perspective drawings of exemplary components of atrajectory detection and analysis system. The figures provided toillustrate types of components in a trajectory system and not mean tolimit various form factors and configurations of these components. Forinstance, the locations, sizes and form factors of these componentscould look substantially different if they were integrated into a golfbag. Further, every component of the system need not be included inevery embodiment. For instance, the sound output device 211 may beeliminated in some designs or made substantially smaller, which couldalter the form factor of the design.

In FIGS. 15A-15C, a camera 201 used in a machine vision system, a touchscreen display 210, a computer 202 and a sound projection device 211 areintegrated into a housing 300 with a support chassis 301. The system 100may also include an amplifier for the speaker 211 (not shown).

Wheels 304 are attached to the chassis 301 to allow the system 100 to beeasily moved and positioned for use. In general, the chassis of devicesof the present invention may be designed with a weight and a formfactor, which may facilitate transport, storage and unobtrusive set-up,calibration and operation of the device. For instance, the deviceincludes a handle 303 attached to panels 300 comprising the housing thatmay be used to move the device and which may aid in set-up and storageof the device.

The speaker 211 takes up a large portion of the internal volume of thesystem. In one embodiment, a travel system may be used that incorporatesa portable computer system such as laptop that is connected to a machinevision system with the camera 201. To use the travel system, it may beplaced on top of a support platform, such as a tripod, a table, a chairor even coupled to a golf bag or golf cart. The travel system mayprovide feedback information via a wireless communication interface toaudio device, such as an “earbud,” worn by the player or wearable feedback device. In another embodiment, the travel system may generateoutput signals that may be routed through a portable audio system (e.g.,a boom box) for amplification via speakers on the audio system toprovide feedback information.

FIG. 16 is an information flow diagram for a trajectory detection andanalysis system of the present invention. A sensor system 502, which maycomprise emitters 506 and detectors 506, receives physical information507. The physical information 507 may be energy signals reflected from atracked object 508, such as a golf ball. In the case where sensors aremounted to the tracked object 508, then the physical information 507 maybe sent as signals from the sensors to a detector 504. Typically, thephysical information 508 is transmitted through a medium such as air.

The sensor system 502 may convert the physical information 507 to sensordata signals 509. For instance, a charge-coupling device generateselectronic signals in response to photons striking a sensor array. Thesensor data signals 509 may be sent through a wired or wirelessconnection to a sensor interface 510, which provides signalconditioning. The signal conditioning may be needed to allow the sensordata 509 to be processed. For instance, prior to analysis, video framedata may be digitized by a video capture card.

In 513, the conditioned signals 511 may be processed according to systemcontrol software and according to trajectory analysis software 513 usingset-up and control inputs 512 that have been input into the system. Thesystem control software 513 may analyze portions of the data 511 todetermine whether the sensor system 502 is operating properly.Based-upon the analysis of the data 511, the system control software mayprovide calibration instructions and other operational instructions tothe sensor system which may be transmitted to the sensors via the sensorinterface 510.

The trajectory analysis software 513 may be used to process theconditioned signals 511 and generate trajectory parameters. Thetrajectory parameters may be used to generate feedback information. Thefeedback information may be one or more trajectory parameters or acombination of trajectory parameters, such as a ratio of trajectoryparameters or a product of trajectory parameters that may be useful to asystem client in improving their trajectory skills.

Depending such factors as the application (trajectory of a specific typeof object), the set-up and components of the system, the environment inwhich the system is used and what portion of the trajectory of an objectthe device is used to measure, the present invention may providefeedback to the player nearly immediately, within a second or within 10seconds as measured from some time state along the trajectory that hasbeen analyzed by the system. For instance, when information on thebeginning of the trajectory is directly generated by the system, thenthe time to provide feedback may be measured from the time when thetrajectory is initiated and then first detected by the system. Wheninformation on the end of the trajectory is directly measured, then thetime to provide feedback may be measured from the time to when thetrajectory has neared completion and has been detected by the system.

The feedback information may be sent as feedback information parameters516 to one or more device interfaces 517. The device interfaces 517 maycommunicate with a plurality of feedback devices. The device interfaces517, which may include device drivers, may transmit device data/commands518 to a feedback device interface 519 located on each feedback device.The device data/commands 518 may be used to control the operation of thefeedback devices. The output from the feedback device may also bemodified using set-up/control inputs 520 that may vary for each device.

The feedback devices may output the feedback information parameters 516received as device data 518 in one of an audio, visual or kinetic format521 depending on the capabilities of the feedback device. For example,the device interface 517 may send device data/commands 518 to a displaythat allows a numeric value of a feedback information parameter 516 tobe viewed on the display by one of the system clients 522, such asplayers, coaches and spectators. As another example, a device interface517 may send device data/commands 518 to an audio output device thatallows feedback information parameters 516 to be output in an audioformat to one or more of the system clients 522.

The feedback parameters 516 generated from the trajectory analysissoftware 513 and other raw data generated from the sensor system 502 maybe sent to session storage 515. The session storage 515 may accumulatetrajectory data from a plurality of trajectories generated during atrajectory session for one or more players. All of a portion of thetrajectory data 514 may be sent to archival storage 525 when the sessionhas been completed. For example, only a portion of the raw data, such asvideo frame data, may be sent to archival storage. Further, the data maybe filtered for bad data prior to being sent to archival storage 525.The archival storage 525 may include a database used to relatetrajectory data from one or more trajectory sessions to the conditionsof the trajectory session, such as time place and location, and playeridentification information.

The archival data 524 and session data 514 may be used to provide one ormore services 523 including but not limited to 1) a session record oftrajectory parameters, 2) session diagnostics, 3) prescription forimprovement, 4) a history comparison of trajectory data from differentsessions, 5) individual/group comparisons of trajectory session data, 6)video analysis and editing tools, 7) simulations (e.g., predicting aplayer's driving distance improvement based upon changing one or more oftheir swing parameters and 8) entertainment. As an example ofentertainment, a player's trajectory average trajectory parameters andvariability may be used in trajectory simulations for a video golf gameor another game where the parameters have been measured. Two playersthat have used the system 100 may both enter their parameters andcompete against one another in the video game. The player may also usethe game to see how they match up against professional or other athleteswho have had their trajectory parameters defined.

Output from the data services 523 may be converted to a portable record527, such as print-out from a printer, or may be formatted for viewingon a graphical interface 528. The graphical interface may also include astorage capacity allowing data to be viewed at a later time. The outputfrom the data services 523, such as a portable record 527 or informationviewed on the graphical interface 528, may be used by the system clients522. The data services 523 may also be provided via a data mininginterface 526. The data mining interface 526 may include analysis toolsand a graphical interface. When the archival storage is remotelyaccessible, it may be used to access archived data 524 via a remoteconnection, such as from the Internet.

Information passed between the different components in the system may betransmitted using a number of different wired and wireless communicationprotocols. For instance, for wire communication, USB compatible,Firewire compatible and IEEE 1394 compatible hardware communicationinterfaces and communication protocols may be used. For wirelesscommunication, hardware and software compatible with standards such asBluetooth, IEEE 802.11a, IEEE 802.11b, IEEE 802.11x (e.g. other IEEE802.11 standards such as IEEE 802.11c, IEEE 802.11d, IEEE 802.11e,etc.), IrDA, WiFi and HomeRF.

Although the foregoing invention has been described in detail by way ofillustration and example for purposes of clarity and understanding, itwill be recognized that the above described invention may be embodied innumerous other specific variations and embodiments without departingfrom the spirit or essential characteristics of the invention. Certainchanges and modifications may be practiced, and it is understood thatthe invention is not to be limited by the foregoing details, but ratheris to be defined by the scope of the appended claims.

1. A system for analyzing a trajectory of a basketball, the devicecomprising: one or more cameras for recording video frame data used tocharacterize a trajectory of a basketball shot by a human; a logicdevice designed or configured to i) receive the video frame data, ii)generate trajectory parameters that characterize one or more states ofthe basketball along its trajectory and iii) generate feedbackinformation using the trajectory parameters; and one or more feedbackoutput mechanisms for providing the feedback information to the humanwherein the feedback information is related to one or more of thefollowing trajectory parameters: 1) an angle of the trajectory relativeto a plane of a basketball hoop when the basketball is proximate to thebasketball hoop, 2) a point on the trajectory relative to a fixed pointwithin the plane of the basketball hoop when the basketball is proximateto the basketball hoop.
 2. The system of claim 1 wherein the fixed pointis a desired target location within the plane of the basketball hoop. 3.The system of claim 2 wherein the desired target location is within aperimeter of the basketball hoop and is a distance from a geometriccenter of the hoop.
 4. The system of claim 1 wherein the system isconfigured to provide feedback information that allows the human tolearn to shoot a shot toward the desired target location.
 5. The systemof claim 1, wherein the one or more cameras is located on a portabledevice.
 6. The system of claim 1, where portable device is a cell-phoneor laptop.
 7. The system of claim 6, wherein software is downloaded tothe portable device to allow the device to perform as a machine visionsystem.
 8. A training device for use in basketball, said training devicecomprising: a mechanism designed to be coupled to a basketball hoop saidmechanism configured to cause shots proximate to a front of thebasketball hoop that pass through the hoop without the mechanisminstalled to be deflected away from the basketball hoop to encourage auser to aim their shots deeper in the basketball rim behind thegeometric center of the hoop.
 9. The training device of claim 8, whereinthe mechanism extends around a portion of the circumference ofbasketball hoop.
 10. The training device of claim 8, wherein themechanism is configured to allow shots that clear the mechanism todeflect to deflect off a back portion of the basketball rim and passthrough the hoop.
 11. A system for analyzing a trajectory of abasketball, the device comprising: a first device including: a) one ormore cameras for recording video frame data used to characterize atrajectory of a basketball shot by a human; b) a logic device designedor configured to i) receive the video frame data, ii) generatetrajectory parameters that characterize one or more states of thebasketball along its trajectory and iii) generate feedback informationusing the trajectory parameters; c) one or more feedback outputmechanisms for providing the feedback information to the human whereinthe feedback information is related to one or more of the followingtrajectory parameters: 1) an angle of the trajectory relative to a planeof a basketball hoop when the basketball is proximate to the basketballhoop, 2) a point on the trajectory relative to a fixed point within theplane of the basketball hoop when the basketball is proximate to thebasketball hoop and d) a first wireless interface a second deviceincluding a) a video display, b) a storage device for storing datagenerated by the first device, c) a second wireless interface configuredto communicate with the first device via the first wireless interfaceand to upload data to a remote device separate from the first device.